These are popular ideas in many places, but here are just some things to consider:
1a) If you town bans short-term rentals but the next town over doesn't, then guess what - the investors just migrate and you haven't actually changed much.
1b) Highest and best use is a really important concept. There are properties that make for not great permanent dwellings but are great short-term rentals. When you put artificial restrictions in place, it doesn't actually help supply.
2) There is so much money here in the US that even banning foreign ownership doesn't matter much. I live in a tourist / second-home market and it's people from the region who are buying up the investments.
3a) My community went to relaxed zoning years ahead of the state. Helped a little, but not as much as everyone hoped. Turns out that it is still expensive to build multi-family, ADUs, etc and not a fit for every life need.
3b) While zoning changes are good, I continue to hammer on income / jobs as a bigger factor in many markets. Don't come at me with SFO or some other example - every market is going to be different. But in places like mine, the make up of the economy is a bigger factor to affordability than zoning or these other changes. Fixing the whole regional economy is not a simple problem and it doesn't campaign well in political stump speeches like "fix zoning" does.